Consider the combination of $2$ capacitors $C _{1}$ and $C _{2},$ with $C _{2}> C _{1},$ when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ time the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{ C _{2}}{ C _{1}}$
JEE MAIN 2021, Diffcult
Download our app for free and get started
When connected in parallel $C _{ eq }= C _{1}+ C _{2}$
When in series
$C _{ eq }^{\prime}=\frac{ C _{1} C _{2}}{ C _{1}+ C _{2}}$
$C _{1}+ C _{2}=\frac{15}{4}\left(\frac{ C _{1} C _{2}}{ C _{1}+ C _{2}}\right)$
$4\left( C _{1}+ C _{2}\right)^{2}=15 C _{1} C _{2}$
$4 C _{1}{ }^{2}+4 C _{2}^{2}-7 C _{1} C _{2}=0$
dividing by $C _{1}{ }^{2}$
$4\left(\frac{ C _{2}}{ C _{1}}\right)^{2}-\frac{7 C _{2}}{ C _{1}}+4=0$
Let $\frac{ C _{2}}{ C _{1}}= x$
$4 x^{2}-7 x+4=0$
$b ^{2}-4 ac =49-64<0$
No solution exits981-s782
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1To form a composite $16\,\mu F,\;1000\,V$ capacitor from a supply of identical capacitors marked $8\,\mu F,\;250\,V$, we require a minimum number of capacitorsView Solution
- 2A spherical conductor of radius $2m$ is charged to a potential of $120\, V$. It is now placed inside another hollow spherical conductor of radius $6m$. Calculate the potential to which the bigger sphere would be raised......$V$View Solution
- 3View SolutionThe equivalent capacitance of the combination shown in the figure is :
- 4View SolutionThree different dielectrics are filled in a parallel plate capacitor as shown. What should be the dielectric constant of a material, which when fully filled between the plates produces same capacitance?
- 5The two plates $X $ and $Y$ of a parallel plate capacitor of capacitance $C$ are given a charge of amount $Q$ each. $X$ is now joined to the positive terminal and $Y$ to the negative terminal of a cell of $emf$ $E = Q/C$.View Solution
- 6The electrostatic potential inside a charged spherical ball is given by $\phi= a{r^2} + b$ where $r$ is the distance from the centre and $a, b$ are constants. Then the charge density inside the ball is:View Solution
- 7Potential at a point $x$-distance from the centre inside the conducting sphere of radius $R$ and charged with charge $Q$ isView Solution
- 8Two parallel plate capacitor with different plate seperation but the same capacitance are connected in series to a battery. Both capacitors are filled with air. The quantity that is $NOT$ the same for both the capacitors when they are fully charged isView Solution
- 9Two point charges $4\,\mu C$ and $ - 1\,\mu C$ are kept at a distance of $3\ m$ from each other. What is the electric potential at the point where the electric field is zero?......$V$View Solution
- 10In an insulated parallel-plate capacitor of capacitance $C$, the four surfaces have charges $Q_1, Q_2, Q_3$ and $Q_4$ as shown. The potential difference between the plate isView Solution
